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 A002508 Expansion of a modular function for Gamma_0(6). (Formerly M1910 N0754) 2
 1, -2, 9, -4, 28, 18, 118, 80, 504, 466, 1631, 2160, 5466, 7498, 17658, 25088, 51944, 78660, 149099, 226544, 412920, 627830, 1090006, 1671840, 2796805, 4263984, 6969690, 10555224, 16836620, 25396506, 39699240, 59409184, 91460952, 135795598, 205951071, 303740496, 454672142 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 3..1000 Morris Newman, Construction and application of a class of modular functions (II). Proc. London Math. Soc. (3) 9 1959 373-387. Morris Newman, Construction and application of a class of modular functions, II, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible] FORMULA eta(z)^2*eta(6z)^22/(eta(2z)^10*eta(3z)^14). Euler transform of period 6 sequence [ -2, 8, 12, 8, -2, 0, ...]. - Michael Somos, Nov 10 2005 a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(27/4) * 3^(17/4) * n^(3/4)). - Vaclav Kotesovec, Apr 09 2018 MATHEMATICA QP = QPochhammer; s = QP[q]^2*QP[q^6]^22/(QP[q^2]^10*QP[q^3]^14) + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 30 2015, adapted from PARI *) PROG (PARI) {a(n)=local(A); if(n<3, 0, n-=3; A=x*O(x^n); polcoeff( eta(x+A)^2*eta(x^6+A)^22/ eta(x^2+A)^10/eta(x^3+A)^14, n))} /* Michael Somos, Nov 10 2005 */ CROSSREFS Reciprocal series to A002507. Cf. A002509. Sequence in context: A302451 A220416 A054789 * A249596 A038215 A264110 Adjacent sequences:  A002505 A002506 A002507 * A002509 A002510 A002511 KEYWORD sign,easy AUTHOR EXTENSIONS More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001 STATUS approved

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Last modified August 1 05:04 EDT 2021. Contains 346384 sequences. (Running on oeis4.)